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Let S and T be subsets of a vector space, V. Which of the following statements are true? Give a proof or a counterexample.

a) Sp(S n T)=Sp(S) n Sp(T)

b) Sp(S u T)=Sp(S) u Sp(T)

c) Sp(S u T)=Sp(S) + Sp(T)

For a) i've said its false, and my counter-example is S={(1,0)} and T={(0,1)} for R^2. But then I get LHS= Span of the empty set? Is this correct?

and from the answers i know that b)is false and c)is true but i have no idea how to prove this.

also just in general, what is the difference between "+" and "u" in this situation?

Any help would be appreciated! thank you!